Higher Spin Gauge Theories

Abstract

Vasiliev's equations are, to this day, the only known set of consistent and non-linear equations that describe, after linearisation around four dimensional (anti-)de Sitter spacetime, the free propagation of an infinite set of higher-spin gauge fields featuring the graviton. These last two years, new results have been derived in Higher Spin (HS) theory. They partly confirmed some expectations on the subject and they also showed that more work is required for a better understanding of the weak-field expansion of Vasiliev's equations around (A)dS4. On the one hand, the holographic reconstruction of a theory from the free O(N) model in three dimensions seems to reproduce, as expected from the HS/CFT conjecture, a non-abelian gauge theory of higher spin fields in (A)dS4. On the other hand, the Vasiliev equations display some seemingly unavoidable non-localities in their perturbative regime around (A)dS4. These last results raise some questions regarding the status of the HS4/CFT3 duality. In parallel, recent works performed in the light-cone gauge bring back to the scene some results obtained by Metsaev in the early nineties, pointing to the existence of a consistent and interacting HS theory in flat background